Two chilling videos kept out of sight for decades could be the key to persuading a court next month that Saudi Arabia was behind the Sept. 11, 2001 terrorist attacks, and that victims’ families have amassed enough evidence to continue their years-long legal battle, according to family members of victims. Federal Appeals Court judges in lower Manhattan will hear oral arguments for the first time Oct. 7 that connect the men in those videos to the Saudi government and its intelligence services, as well as the horrific attacks of that day. Both videos involve the same enigmatic figure, Omar al-Bayoumi,...